Table Of ContentMODELING FINANCIAL
TIME SERIES WITH
S-PLUS®
Springer Science+Business Media, LLC
Eric Zivot Jiahui Wang
MODELING FINANCIAL
TIME SERIES WITH
S-PLUS®
i
Springer
Enc Zivot Jiahui Wang
DeparbnentofEconorrrics Ronin Capital LLC
University of Washington 230 S. LaSalle Street
Seattle, WA 98195-3330 4th Floor
USA Chicago, IL 60604
[email protected] USA
[email protected]
Library of Congress Cataloging-in-Publication Data
Zivot, Eric.
Modelmg financial time series with S-Plus I Eric Zivot, Jiahui Wang.
p. em.
Includes bibliographical references and index.
ISBN 978-0-387-91624-8 (pbk. : alk. paper)
1. Finance-Mathematical methods. 2. Time series analysis. 3. Finance-Econometric
models. 4. S-Plus. I. Wang, Jiahm. II. Title.
HGJ06 .Z584 2003
332'.01 '.51955-dc21 2002026657
ISBN 978-0-387-91624-8 ISBN 978-0-387-21763-5 (eBook)
DOI 10.1007/978-0-387-21763-5
Printed on acid-free paper.
© Springer Science+Business Media New York 2003
Originally published by Springer-Verlag Berlin Heidelberg New York in 2003
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher ( Springer Science+B usiness Media, LLC ), except for brief excerpts
in connection with reviews or scholarly analysis. Use in connection with any torm of information
storage and retneval, electronic adaptation, computer software, or by similar or dissimilar methodology
now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if they
are not identified as such, is not to be taken as an expression of opinion as to whether or not they are
subject to proprietary rights.
9 8 7 6 5 4 3 2 (Corrected printing, 2003) SPIN10941423
Typesetting: Pages created by the authors using a Springer TE X macro package.
Preface ix
Hui Huang with help from many people. In particular, Jan Beran wrote
many of the long memory functions while acting as a consultant to Insight
ful. Siem Jan Koopman helped to incorporate the SsfPack functions into
S-PLUS and to write the chapter on state space models. Alexander McNeil
and Rene Carmona graciously provided background material and S-PLUS
examples for the material in the chapter on modeling extreme values. A
number of people were helpful in proofreading the book and testing the soft
ware. Particular thanks go to Andrew Bruce, Chuck Curry, Zhuanxin Ding,
Ruud Koning, Steve McKinney, David Weitzel, Quan Wen and Bingcheng
Yan.
Typographical Conventions
This book obeys the following typographic conventions:
• The italic font is used for emphasis, and also for user-supplied vari
ables within UNIX, DOS and S-PLUS commands.
• The typewriter font is used for S-PLUS functions, the output of
S-PLUS functions and examples of S-PLUS sessions.
• S-PLUS objects of a specified class are expressed in typewriter font
enclosed in quotations " ". For example, the S-PLUS timeSeries
function creates objects of class "timeSeries".
Displayed S-PLUS commands are shown with the prompt character>. For
example
> summary(ols.fit)
S-PLUS commands that require more than one line of input are displayed
with the continuation prompt indicated by + or Continue string: . The
S-PLUS output and plots in this book were generated from S+FinMetrics
Version 1.0 and S-PLUS Version 6.0 release 2 for Windows. The S-PLUS
output and "timeSeries" objects were generated with the options settings
> options(width=60)
> options(time.zone="GMT")
In some cases, parts of long output from S-PLUS functions is omitted and
these lines are indicated by
Some of the output has been hand edited to avoid line overflow.
Preface
What Is the Book and Why Was It Written?
This book is a guide to analyzing and modeling financial time series using
S-PLUS and S+FinMetrics. It is a unique blend of econometric theory, fi
nancial models, data analysis, and statistical programming. It serves as a
user's guide for Insightful's S+FinMetrics module of statistical functions
for financial time series analysis and financial econometrics as well as a gen
eral reference for models used in applied financial econometrics. The format
of the chapters in the book is to give a reasonably complete description of
a statistical model and how it works followed by illustrations of how to
analyze the model using S-PLUS and the functions in S+FinMetrics. In
this way, the book stands alone as an introduction to financial time series
analysis as well as a user's guide for S+FinMetrics. It also highlights the
general analysis of time series data using the new time series objects in
S-PLUS 6.
Intended Audience
This book is written for a wide audience of individuals who work, do re
search or study in the areas of empirical finance and financial econometrics.
The field of financial econometrics has exploded over the last decade, and
this book represents an integration of theory, methods and examples us
ing the S-PLUS modeling language to facilitate the practice of financial
econometrics. This audience includes researchers and practitioners in the
finance industry, academic researchers in economics and finance, and ad-
vi Preface
vanced MBA and graduate students in economics and finance. Researchers
and practitioners in the finance industry who already useS-PLUS and de
sire more functionality for analyzing and modeling financial data will find
this text useful. It is also appropriate for financial analysts who may not
be familiar with S-PLUS but who desire an integrated and open statistical
modeling and programming environment for the analysis of financial data.
This guide is useful for academic researchers interested in empirical finance
and financial econometrics. Finally, this book may be used as a textbook
or a textbook companion for advanced MBA and graduate level courses in
empirical finance and financial econometrics.
Audience Background
It is assumed that the reader has a basic familiarity with S-PLUS at the level
of Krause and Olson (2002) and a background in mathematical statistics
at the level of Hogg and Craig {1994), is comfortable with linear algebra
and linear regression, and has been exposed to basic time series concepts as
presented in Harvey {1993) or Franses {1998). Most importantly, the book
assumes that the reader is interested in modeling and analyzing financial
time series.
Overview of the Book
The chapters in the book cover univariate and multivariate models for ana
lyzing financial time series using S-PLUS and the functions in S+FinMetrics.
Chapter one gives a general overview of the use of S-PLUS 6 and highlights
certain aspects of the language for statistical modeling. Chapter two intro
duces the new time series objects inS-PLUS 6 and illustrates the specifica
tion, manipulation and visualization of these objects. Chapter three surveys
time series concepts used throughout the book. Chapters four through eight
cover a variety of topics in the modeling of univariate financial time series,
including testing for unit roots, extreme value theory, time series regression
models, GARCH models of volatility, and long memory models. Chapter
nine introduces rolling analyses of time series models and covers related
topics such as technical analysis of financial time series and moving aver
age methods for high frequency data. Chapters ten through fifteen cover
models for the analysis of multivariate financial time series. Topics include
systems of regression equations, classical and Bayesian vector autoregres
sive models, cointegration, factor models, multivariate GARCH models,
and state space models. Chapter 16 covers aspects of modeling time series
arising from fixed income financial assets. Chapter 17, written by Victor
Yohai and Jiahui Wang, describes robust REGARIMA models that allow
for structural change.
Preface vii
What Is S+FinMetrics?
S+FinMetrics is an S-PLUS module for the econometric modeling and pre
diction of economic and financial time series. With some 600 functions,
version 1.0 of S+FinMetrics offers the following functionality:
• Easy-to-use Trellis plots for multivariate time series
• Time series manipulations such as missing value interpolation, dis
aggregation, differences, distributed lags and polynomial distributed
lags
• Rolling sample statistics such as variance, maximum, and minimum
• Moving average operators for both regularly spaced and irregularly
spaced time series
• Common technical analysis measures and indicators
• Statistical tests for normality, autocorrelation, heteroskedasticity, mul
ticollinearity, GARCH effects, and long memory
• Extreme value theory models based on generalized extreme value and
generalized Pareto distributions as well as copulas
• Autoregressive distributed lag regression models
• White and Newey-West corrections for heteroskedasticity and serial
correlation
• Robust estimation of REG-ARIMA models and robust detection of
level shifts, trend breaks, and outliers
• Rolling and recursive regression
• Generic rolling models for back-testing
• Long memory fractional ARIMA and SEMIFAR models
• Univariate GARCH models including long memory FIGARCH and
FIEGARCH models
• Multivariate GARCH models
• Linear and nonlinear systems of regression equations
• Classical and Bayesian vector autoregression models
• Tests for unit roots and cointegration
• Vector error correction models
viii Preface
• State space models and efficient estimation, prediction, smoothing,
and simulation using the Kalman filter
• Statistical multifactor models for large data sets based on asymptotic
principal components
• Term structure interpolation
S+FinMetrics incorporates functions from S+GARCH, the EVIS library
of functions for modeling extreme values created by Alexander McNeil,
the EVANESCE library of functions for modeling extreme values utilizing
copulas created by Rene Carmona, and the SsfPack C library of state space
modeling functions created by Siem Jan Koopman. S+GARCH was originally
developed by Zhuanxin Ding, Hong-Ye Gao, Doug Martin, Jiahui Wang
and Yihui Zhan. The S+FinMetrics function arima.rob was written by
Ana Bianco, Marta Garcia Ben, Elena Martinez and Victor Yohai. The
S+FinMetrics long memory modeling functions FAR, FARIMA, SEMIFAR and
fgarch were developed by Jan Beran, Andrew Bruce, Don Percival, Alan
Gibbs and Jiahui Wang and supported by NSF grant DMI-9801614 to
Insightful Corporation (formerly MathSoft, Inc.). Hu McCulloch kindly
provided the term structure data included with S+FinMetrics, and James
MacKinnon provided data sets for the response surface critical values for
the Dickey-Fuller and Phillips-Ouliaris distributions.
Contact Information and Website
The authors are responsible for all of the material in the book except the
material on robust change detection, which was written by Victor Yohai.
Eric Zivot is primarily responsible for chapters 2-6, 9-12 and 14-15 and
Jiahui Wang is primarily responsible for chapters 1, 7-8, 13, and 16. The
authors may be contacted by electronic mail at
[email protected]
[email protected]
and welcome feedback and suggestions for improvements to the contents of
the book. The website for the book is located on the Insightful Corporation
website at
http://www.insightful.com/support/finmetrics10
Acknowledgements
This book would not have been written without the support and encour
agement from Insightful Corporation. The idea for the S+FinMetrics mod
ule was conceived by Douglas Martin and the authors. The development of
S+FinMetrics was completed at Insightful by Jiahui Wang, Quan Wen and
